As wireless communication applications evolve from traditional multipath environments to high-mobility scenarios like unmanned aerial vehicles, multiplexing techniques have advanced accordingly. Traditional single-carrier frequency-domain equalization (SC-FDE) and orthogonal frequency-division multiplexing (OFDM) have given way to emerging orthogonal timefrequency space (OTFS) and affine frequency-division multiplexing (AFDM). These approaches exploit specific channel structures—e.g., Toeplitz-structured multipath channel matrix for OFDM and SC-FDE or doubly selective channels for OTFS and AFDM—to diagonalize or sparsify the effective channel, thereby enabling low-complexity detection. However, their reliance on these structures significantly limits their robustness in dynamic, real-world environments. To address these challenges, this paper studies a random multiplexing technique that is decoupled from the physical channels, thereby enabling its application to arbitrary norm-bounded and spectrally convergent channel matrices. Random multiplexing achieves statistical fading-channel ergodicity for transmitted signals by constructing an equivalent input-isotropic channel matrix in the random transform domain. It guarantees the asymptotic replica MAP bit-error rate (BER) optimality of AMP-type detectors for linear systems with arbitrary norm-bounded, spectrally convergent channel matrices and signaling configurations, under the unique fixed point assumption. A low-complexity cross-domain memory AMP (CD-MAMP) detector is considered for random multiplexing systems, leveraging the sparsity of the time-domain channel and the input isotropy of the equivalent channel. Optimal power allocations are derived to minimize the replica MAP BER and maximize the replica constrained capacity of random multiplexing systems, respectively. The optimal coding principle and replica constrained-capacity optimality of CD-MAMP detector are investigated for random multiplexing systems. Additionally, the versatility of random multiplexing in diverse wireless applications is explored. Numerical results are presented to validate the theoretical findings.

This paper introduces a random modulation technique that is decoupled from the channel matrix, allowing it to be applied to arbitrary norm-bounded and spectrally convergent channel matrices. The proposed random modulation constructs an equivalent dense and random channel matrix, ensuring that the signals undergo sufficient statistical channel fading. It also guarantees the asymptotic replica maximum a posteriori (MAP) bit-error rate (BER) optimality of approximate message passing (AMP)-type detectors for linear systems with arbitrary norm-bounded and spectrally convergent channel matrices when their state evolution has a unique fixed point. Then, a lowcomplexity cross-domain memory approximate message passing (CD-MAMP) detector is proposed for random modulation, leveraging the sparsity of the time-domain channel and the randomness of the random transform-domain channel. Furthermore, the optimal power allocation schemes are derived to minimize the replica MAP BER and maximize the replica constrained capacity of random-modulated linear systems, assuming the availability of channel state information (CSI) at the transceiver. Numerical results show that the proposed random modulation can achieve BER and block-error rate (BLER) performance gains of up to$2 \sim 3 \mathbf{d B}$compared to existing OFDM/OTFS/AFDM with 5G-NR LDPC codes, under both average and optimized power allocation.

Approximate Message Passing (AMP) type algorithms are widely used for signal recovery in high-dimensional noisy linear systems. Recently, a principle called Memory AMP (MAMP) was proposed. Leveraging this principle, the gradient descent MAMP (GD-MAMP) algorithm was designed, inheriting the strengths of AMP and OAMP/VAMP. In this paper, we first provide an overflow-avoiding GD-MAMP (OA-GD-MAMP) to address the overflow problem that arises from some intermediate variables exceeding the range of floating point numbers. Second, we develop a complexity-reduced GD-MAMP (CR-GD-MAMP) to reduce the number of matrix-vector products per iteration by 1/3 (from 3 to 2) with little to no impact on the convergence speed.

Approximate message passing (AMP) algorithms are iterative methods for signal recovery in noisy linear systems. In some scenarios, AMP algorithms need to operate within a distributed network. To address this challenge, the distributed extensions of AMP (D-AMP, FD-AMP) and orthogonal/vector AMP (D-OAMP/D-VAMP) were proposed, but they still inherit the limitations of centralized algorithms. In this letter, we propose distributed memory AMP (D-MAMP) to overcome the IID matrix limitation of D-AMP/FD-AMP, as well as the high complexity and heavy communication cost of D-OAMP/D-VAMP. We introduce a matrix-by-vector variant of MAMP tailored for distributed computing. Leveraging this variant, D-MAMP enables each node to execute computations utilizing locally available observation vectors and transform matrices. Meanwhile, global summations of locally updated results are conducted through message interaction among nodes. For acyclic graphs, D-MAMP converges to the same mean square error performance as the centralized MAMP.

The widely applied orthogonal frequency division multiplexing (OFDM) system naturally contains oversampled cyclic prefixes (CP) in the generation process, which provide a wealth of environmental information and higher distance resolution for integrated sensing and communication (ISAC) but is underutilized. Therefore, we develop a compressed sensing (CS) model with oversampled CP, reaching the higher distance resolution limit corresponding to the sample rate of the analog-to-digital converter (ADC) than the fixed signal bandwidth. Since the measurement matrix formed by shifting adjacent oversampled CP pairs is ill-conditioned, we proposed random modulation and random extraction from multiple oversampled CP to increase the validity of the observations. To exploit the channel fading characteristics and sparsity of scattering points, we propose an element-by-element demodulator based on the orthogonal approximate message passing (OAMP) algorithm, called the element-wise OAMP (E-OAMP) algorithm. The simulation results validate the outstanding performance of the proposed algorithm over traditional CS algorithms.

Approximate message passing (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state evolution. However, state evolution does not necessarily guarantee the convergence of iterative algorithms. To solve the convergence problem of AMP-type algorithms in principle, this paper proposes a memory AMP (MAMP) under a sufficient statistic condition, named sufficient statistic MAMP (SS-MAMP). We show that the covariance matrices of SS-MAMP are L-banded and convergent. Given an arbitrary MAMP, we can construct the SS-MAMP by damping, which not only ensures the convergence, but also preserves the orthogonality, i.e., its dynamics can be correctly described by state evolution.

People have enjoyed solving puzzles for decades because of the challenge and the satisfaction derived from solving problems. However, although previous researches focused on the puzzle’s complexity, strategy, and solving automatically, few studies worked on sorting out puzzles from a solvability way related to the stochastic elements among the solving process. The contribution of the study is twofold. Firstly, a single-agent stochastic puzzle definition is established via Minesweeper testbed, a well-known puzzle synonymous with Microsoft Windows. Secondly, this study proposes an artificial intelligence (AI) solver based on the obtained information on the board, called the ‘PAFG’ strategy, which stands for the primary reasoning, the advanced reasoning, the first action strategy, and the guessing strategy. The first two strategies take advantage of knowledge-based rules and linear system transformation (Gauss–Jordan elimination algorithms) to determine the probability of making a move independently. The last two strategies explore the beginning and ways to determine hidden puzzle states to enhance the winning rate of the AI solver. The experimental simulation of various configurations and the AI solver with PAFG strategy yielded a high-level winning rate of 96.4%, 86.3%, and 45.6% for the 9×9|10, 16×16|40, and 16×30|99 Minesweeper board configuration, which is comparable to the state of the art study. Thus, such an AI solver could contribute to classifying single-agent stochastic puzzles and establishing the boundary of the puzzle-solving and game-playing paradigm.

Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. AMP only applies to independent identically distributed (IID) transform matrices, but may become unreliable (e.g., perform poorly or even diverge) for other matrix ensembles, especially for ill-conditioned ones. To solve this issue, orthogonal/vector AMP (OAMP/VAMP) was proposed for general right-unitarily-invariant matrices. However, the Bayes-optimal OAMP/VAMP (BO-OAMP/VAMP) requires a high-complexity linear minimum mean square error (MMSE) estimator. This prevents OAMP/VAMP from being used in large-scale systems. To address the drawbacks of AMP and BO-OAMP/VAMP, this paper offers a memory AMP (MAMP) framework based on the orthogonality principle, which ensures that estimation errors in MAMP are asymptotically IID Gaussian. To realize the required orthogonality for MAMP, we provide an orthogonalization procedure for the local memory estimators. In addition, we propose a Bayes-optimal MAMP (BO-MAMP), in which a long-memory matched filter is used for interference suppression. The complexity of BO-MAMP is comparable to AMP. To asymptotically characterize the performance of BO-MAMP, a state evolution is derived. The relaxation parameters and damping vector in BO-MAMP are optimized based on state evolution. Most crucially, the state evolution of the optimized BO-MAMP converges to the same fixed point as that of the high-complexity BO-OAMP/VAMP for all right-unitarily-invariant matrices, and achieves the Bayes optimal MSE predicted by the replica method if its state evolution has a unique fixed point. Finally, simulations are provided to verify the theoretical results’ validity and accuracy.

Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. However, AMP only applies to independent identically distributed (IID) transform matrices, but may become unreliable for other matrix ensembles, especially for ill-conditioned ones. To handle this difficulty, orthogonal/vector AMP (OAMP/VAMP) was proposed for general right-unitarily-invariant matrices. However, the Bayes-optimal OAMP/VAMP requires high-complexity linear minimum mean square error estimator. To solve the disadvantages of AMP and OAMP/VAMP, this paper proposes a memory AMP (MAMP), in which a long-memory matched filter is proposed for interference suppression. The complexity of MAMP is comparable to AMP. The asymptotic Gaussianity of estimation errors in MAMP is guaranteed by the orthogonality principle. A state evolution is derived to asymptotically characterize the performance of MAMP. Based on the state evolution, the relaxation parameters and damping vector in MAMP are optimized. For all right-unitarily-invariant matrices, the optimized MAMP converges to OAMP/VAMP, and thus is Bayes-optimal if it has a unique fixed point. Finally, simulations are provided to verify the validity and accuracy of the theoretical results.